Embodiments herein generally relate to rollers used to supply continuous webs of printing sheets (rolls of paper) to/from printing devices and more particularly to inertia compensated dancer roll design.
U.S. Pat. No. 3,659,767 to J. R. Martin (hereinafter referred to as “Martin” and fully incorporated herein by reference) discloses a “dancer” roll used in a system for supplying a continuous printing sheet to/from printing devices. The dancer roll is a roller over which the paper (or other printing medium) passes as it is being transported from a roll (medium source) to a printing device or from a printing device to a finishing device. The dancer roll provides a constant tension on the printing medium to attenuate and insulate motion disturbances form reaching the motion crucial areas of the printer.
More specifically, Martin describes that a recurring problem in systems for performing operations on webs of paper, cloth or other suitable material is the regulation of web tension. Such problems may arise in a number of arts such as printing, film and plastic processing, and magnetic tape recording. In the operation of high speed continuous printing presses the problems of regulating web tension are particularly important. Failure to prevent tension changes in a moving paper web results in stretching and shrinking of the web along its length. When this occurs in the region in which the web is being printed it leads to defects in the printed product such as slurring, doubling and ghosting of images, color mis-registration, and if the tension becomes too great, breaking of the web and interruption of operations.
There are several causes of tension fluctuation in printing press operation. These include variations in the web's modulus of elasticity due to material irregularities or changes in temperature or humidity, rolls which have flat spots or are elliptical in cross section, drifting in the speed of the various drive rolls and the supply roll, irregularities in the operation of braking mechanisms, and the operation of flying pasters which join one supply roll to another while the press is in operation.
A number of means have been developed to regulate or control tension, none of which completely solve the problem of preventing transient changes or fluctuations in tension in one region of the web from causing tension changes in other regions. One approach has been to utilize one or more dancer rolls—floating rotating cylinders each of which, when placed between two idler rolls and offset therefrom, constrains the web into a loop and exerts force on the bight of the loop. This force, which may be a result of the weight of the dancer or of a force exerted on the dancer by a spring, a fluid pressure actuated cylinder, or an external weight, or some combination thereof, establishes an average level of tension in the loop. It does not, however, completely compensate for changes in web tension on one side of the dancer which usually cause tension changes on the other side of the dancer.
Martin explains that devices have been developed in which the position of a roller, which changes as the web tension changes, is sensed to produce an input signal for a control circuit. The control circuit may be used to adjust another parameter which can affect web tension such as the speed of the supply roll or of drive rolls thus readjusting the web tension to compensate for the initial change and restoring the dancer to its initial position.
In order to address the foregoing issues, embodiments herein comprise a printing apparatus (e.g., an electrostatographic and a xerographic machine, etc.); an associated method of making a floating roller; and an associated computer program. The apparatus includes a tensioning system having a plurality of rollers. One of the rollers (e.g., a receiver roller) is adapted to receive a web of material from a web supply or a processing machine, and another roller (e.g., an output roller) is adapted to output the web of material to a processing machine or a finishing device. A floating roller is positioned between the receiver roller and the output roller and is adapted to pass the material from the receiver roller to the output roller. The floating roller is mounted to rotate and travel along at least one linear path or pivot around some center to move the floating roller center. The apparatus can further comprise rotating rollers in fixed positions adjacent the floating roller, such that the floating roller moves relative to the rotating rollers to maintain the constant tension on the web of material.
The relationship between mass of the floating roller and rotational inertia of the floating roller controls the tensioning system to maintain a constant tension on the web of material. More specifically, the relationship between mass of the floating roller and rotational inertia of the floating is based on the following equation:
      M    2    ≈            (              1        -                                            T              _                                      a              ⁢                                                          ⁢              3                                Ebw                    )        ⁢                  sin        2            ⁡              (                  α          /          2                )              ⁢                  J        2                    R        2        2            wherein M2 is a mass of the floating roller, J2 is a rotational inertia of the floating roller, R2 is an external radius of the floating roller, E is a Young's modulus of the web of material, b is a thickness of the web of material, w is a width of the web of material, Ta3 is a tension force on the material and α (wrap angle) is an angle at which the web of material contacts the floating roller.
Similarly, a method embodiment of designing a floating roller in a tensioning system adapted to supply a web of material from a web supply to a processing machine comprises inputting an external radius of the floating roller, a measure of elasticity of the material, a thickness of the material, a width of the material, and angles at which the material contacts the floating roller; and adjusting a mass of the floating roller and a rotational inertia of the floating roller such that the floating roller maintains a constant tension on the web of material as the material is passing through the tensioning system based on the following equation:
      M    2    ≈            (              1        -                                            T              _                                      a              ⁢                                                          ⁢              3                                Ebw                    )        ⁢                  sin        2            ⁡              (                  α          /          2                )              ⁢                  J        2                    R        2        2            wherein M2 is the mass of the floating roller, J2 is the rotational inertia of the floating roller, R2 is the external radius of the floating roller, E is a Young's modulus of the web of material, b is the thickness of the web of material, w is the width of the web of material, Ta3 is the tension force on the material and α (wrap angle) is an angle at which the web of material contacts the floating roller.
These and other features are described in, or are apparent from, the following detailed description.